Hybrid vehicles may include an engine, an electric motor, a clutch for placing a power transmitting path between the engine and the electric motor in a power transmitting state and a power cutoff state, and a transmission disposed in a power transmitting path between the electric motor and drive wheels. Patent Document 1 discloses an example of such a hybrid vehicle. When this hybrid vehicle is placed in a motor drive mode in which the electric motor is operated as the vehicle drive power source, the clutch is placed in a released state to prevent a dragging state of the engine. When the hybrid vehicle is placed in an engine drive mode in which the engine is the main vehicle drive power source, on the other hand, the clutch is placed in an engaged state to transmit a drive force of the engine to the drive wheels. Patent Document 1 also describes that the vehicle drive mode is switched from the motor drive mode to the engine drive mode, by placing the clutch in a slipping state to increase a speed of the engine with a torque of the electric motor, to a value at which the engine can be operated by itself, for thereby starting the engine. Patent Document 1 further describes that when the transmission is instructed to be shifted down as a result of an operation of an accelerator pedal during start of the engine, that is, when a so-called “power-on shift-down action” of the transmission is required, the transmission is shifted down after the engine is started. This manner of control reduces a slipping speed of the clutch during an increase in the engine speed, and accordingly reduces the generation of heat by the slipping clutch, making it possible to reduce deterioration of the clutch due to the generated heat.